Mattarei, Sandro (2008) Linear recurrence relations for binomial coefficients modulo a prime. Journal of Number Theory, 128 (1). pp. 4958. ISSN 0022314X
Full content URL: http://dx.doi.org/10.1016/j.jnt.2007.05.003
Documents 

PDF
__network.uni_staff_S2_jpartridge_1s2.0S0022314X0700114Xmain.pdf  Whole Document Restricted to Repository staff only 143kB 
Item Type:  Article 

Item Status:  Live Archive 
Abstract
We investigate when the sequence of binomial coefficients binom(k,i) modulo a prime p, for a fixed positive integer k, satisfies a linear recurrence relation of (positive) degree h in the finite range 0⩽i⩽k. In particular, we prove that this cannot occur if 2h⩽k<p−h. This hypothesis can be weakened to 2h⩽k<p if we assume, in addition, that the characteristic polynomial of the relation does not have −1 as a root. We apply our results to recover a known bound for the number of points of a Fermat curve over a finite field.
Keywords:  binomial coefficient, linear recurrence 

Subjects:  G Mathematical and Computer Sciences > G110 Pure Mathematics 
Divisions:  College of Science > School of Mathematics and Physics 
ID Code:  18505 
Deposited On:  11 Dec 2015 09:03 
Repository Staff Only: item control page